{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T15:00:50Z","timestamp":1772809250536,"version":"3.50.1"},"reference-count":31,"publisher":"American Institute of Mathematical Sciences (AIMS)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["AMC"],"published-print":{"date-parts":[[2016]]},"DOI":"10.3934\/amc.2016030","type":"journal-article","created":{"date-parts":[[2016,8,12]],"date-time":"2016-08-12T11:14:28Z","timestamp":1471000468000},"page":"613-632","source":"Crossref","is-referenced-by-count":3,"title":["Further results on multiple coverings of the farthest-off points"],"prefix":"10.3934","volume":"10","author":[{"given":"Daniele","family":"Bartoli","sequence":"first","affiliation":[]},{"given":"Alexander A.","family":"Davydov","sequence":"additional","affiliation":[]},{"given":"Massimo","family":"Giulietti","sequence":"additional","affiliation":[]},{"given":"Stefano","family":"Marcugini","sequence":"additional","affiliation":[]},{"given":"Fernanda","family":"Pambianco","sequence":"additional","affiliation":[]}],"member":"2321","reference":[{"key":"key-10.3934\/amc.2016030-1","unstructured":"D. Bartoli, A. A. Davydov, M. Giulietti, S. Marcugini and F. Pambianco, Multiple coverings of the farthest-off points and multiple saturating sets in projective spaces, in <em>Proc. XIII Int. Workshop Algebr. Combin. Coding Theory, ACCT2012<\/em>, Pomoria, Bulgaria, 2012, 53-59."},{"key":"key-10.3934\/amc.2016030-2","doi-asserted-by":"publisher","unstructured":"D. Bartoli, A. A. Davydov, M. Giulietti, S. Marcugini and F. Pambianco, Multiple coverings of the farthest-off points with small density from projective geometry, <em>Adv. Math. Commun.<\/em>, <strong>9<\/strong> (2015), 63-85.","DOI":"10.3934\/amc.2015.9.63"},{"key":"key-10.3934\/amc.2016030-3","doi-asserted-by":"publisher","unstructured":"D. Bartoli, G. Faina, S. Marcugini and F. Pambianco, On the minimum size of complete arcs and minimal saturating sets in projective planes, <em>J. Geom.<\/em>, <strong>104<\/strong> (2013) 409-419.","DOI":"10.1007\/s00022-013-0178-y"},{"key":"key-10.3934\/amc.2016030-4","doi-asserted-by":"publisher","unstructured":"E. Boros, T. Sz\u0151nyi and K. Tichler, On defining sets for projective planes, <em>Discrete Math.<\/em>, <strong>303<\/strong> (2005), 17-31.","DOI":"10.1016\/j.disc.2004.12.015"},{"key":"key-10.3934\/amc.2016030-5","unstructured":"R. A. Brualdi, S. Litsyn and V. S. Pless, Covering radius, in <em>Handbook of Coding Theory<\/em> (eds. V.S. Pless, W.C. Huffman and R.A. Brualdi), Elsevier, Amsterdam, 1998, 755-826."},{"key":"key-10.3934\/amc.2016030-6","unstructured":"G. Cohen, I. Honkala, S. Litsyn and A. Lobstein, <em>Covering Codes<\/em>, North-Holland, Amsterdam, 1997."},{"key":"key-10.3934\/amc.2016030-7","doi-asserted-by":"publisher","unstructured":"A. A. Davydov, Constructions and families of covering codes and saturated sets of points in projective geometry, <em>IEEE Trans. Inform. Theory<\/em>, <strong>41<\/strong> (1995), 2071-2080.","DOI":"10.1109\/18.476339"},{"key":"key-10.3934\/amc.2016030-8","doi-asserted-by":"publisher","unstructured":"A. A. Davydov, G. Faina, M. Giulietti, S. Marcugini and F. Pambianco, On constructions and parameters of symmetric configurations $v_k$, <em>Des. Codes Cryptogr.<\/em>, <strong>80<\/strong> (2016), 125-147.","DOI":"10.1007\/s10623-015-0070-x"},{"key":"key-10.3934\/amc.2016030-9","unstructured":"A. A. Davydov, M. Giulietti, S. Marcugini and F. Pambianco, On the spectrum of possible parameters of symmetric configurations, in <em>Proc. XII Int. Symp. Probl. Redundancy Inform. Control Systems<\/em>, Saint-Petersburg, Russia, 2009, 59-64."},{"key":"key-10.3934\/amc.2016030-10","doi-asserted-by":"crossref","unstructured":"A. A. Davydov, M. Giulietti, S. Marcugini and F. Pambianco, New inductive constructions of complete caps in $PG(N,q)$, $q$ even, <em>J. Comb. Des.<\/em>, <strong>18<\/strong> (2010), 176-201.","DOI":"10.1002\/jcd.20230"},{"key":"key-10.3934\/amc.2016030-11","doi-asserted-by":"publisher","unstructured":"A. A. Davydov, M. Giulietti, S. Marcugini and F. Pambianco, Linear nonbinary covering codes and saturating sets in projective spaces, <em>Adv. Math. Commun.<\/em>, <strong>5<\/strong> (2011), 119-147.","DOI":"10.3934\/amc.2011.5.119"},{"key":"key-10.3934\/amc.2016030-12","doi-asserted-by":"publisher","unstructured":"A. A. Davydov, M. Giulietti, S. Marcugini and F. Pambianco, Some combinatorial aspects of constructing bipartite-graph codes, <em>Graphs Combin.<\/em>, <strong>29<\/strong> (2013), 187-212.","DOI":"10.1007\/s00373-011-1103-5"},{"key":"key-10.3934\/amc.2016030-13","doi-asserted-by":"crossref","unstructured":"M. Giulietti, On small dense sets in Galois planes, <em>Electr. J. Combin.<\/em>, <strong>14<\/strong> (2007), #75.","DOI":"10.37236\/993"},{"key":"key-10.3934\/amc.2016030-14","doi-asserted-by":"publisher","unstructured":"M. Giulietti, Small complete caps in $PG(N,q), q$ even, <em>J. Combin. Des.<\/em>, <strong>15<\/strong> (2007), 420-436.","DOI":"10.1002\/jcd.20131"},{"key":"key-10.3934\/amc.2016030-15","doi-asserted-by":"crossref","unstructured":"M. Giulietti, The geometry of covering codes: small complete caps and saturating sets in Galois spaces, in <em>Surveys in Combinatorics<\/em>, Cambridge Univ. Press, 2013, 51-90.","DOI":"10.1017\/CBO9781139506748.003"},{"key":"key-10.3934\/amc.2016030-16","doi-asserted-by":"publisher","unstructured":"M. Giulietti and F. Pasticci, Quasi-perfect linear codes with minimum distance 4, <em>IEEE Trans. Inform. Theory<\/em>, <strong>53<\/strong> (2007), 1928-1935.","DOI":"10.1109\/TIT.2007.894688"},{"key":"key-10.3934\/amc.2016030-17","unstructured":"M. Giulietti and F. Torres, On dense sets related to plane algebraic curves, <em>Ars Combin.<\/em>, <strong>72<\/strong> (2004), 33-40."},{"key":"key-10.3934\/amc.2016030-18","doi-asserted-by":"publisher","unstructured":"H. O. H\u00e4m\u00e4l\u00e4inen, I. S. Honkala, M. K. Kaikkonen and S. N. Litsyn, Bounds for binary multiple covering codes, <em>Des. Codes Cryptogr.<\/em>, <strong>3<\/strong> (1993), 251-275.","DOI":"10.1007\/BF01388486"},{"key":"key-10.3934\/amc.2016030-19","doi-asserted-by":"publisher","unstructured":"H. O. H\u00e4m\u00e4l\u00e4inen, I. S. Honkala, S. N. Litsyn and P. R. J. \u00d6sterg\u00e5rd, Bounds for binary codes that are multiple coverings of the farthest-off points, <em>SIAM J. Discrete Math.<\/em>, <strong>8<\/strong> (1995), 196-207.","DOI":"10.1137\/S0895480193252100"},{"key":"key-10.3934\/amc.2016030-20","doi-asserted-by":"publisher","unstructured":"H. H\u00e4m\u00e4l\u00e4inen, I. Honkala, S. Litsyn and P. \u00d6sterg\u00e5rd, Football pools - a game for mathematicians, <em>Amer. Math. Monthly<\/em>, <strong>102<\/strong> (1995), 579-588.","DOI":"10.2307\/2974552"},{"key":"key-10.3934\/amc.2016030-21","doi-asserted-by":"publisher","unstructured":"H. O. H\u00e4m\u00e4l\u00e4inen and S. Rankinen, Upper bounds for football pool problems and mixed covering codes, <em>J. Combin. Theory Ser. A<\/em>, <strong>56<\/strong> (1991), 84-95.","DOI":"10.1016\/0097-3165(91)90024-B"},{"key":"key-10.3934\/amc.2016030-22","doi-asserted-by":"crossref","unstructured":"J. W. P. Hirschfeld, <em>Projective Geometries over Finite Fields<\/em>, Oxford Univ. Press, 1998.","DOI":"10.1093\/oso\/9780198502951.001.0001"},{"key":"key-10.3934\/amc.2016030-23","doi-asserted-by":"publisher","unstructured":"I. S. Honkala, On the normality of multiple covering codes, <em>Discrete Math.<\/em>, <strong>125<\/strong> (1994), 229-239.","DOI":"10.1016\/0012-365X(94)90164-3"},{"key":"key-10.3934\/amc.2016030-24","unstructured":"I. Honkala and S. Litsyn, Generalizations of the covering radius problem in coding theory, <em>Bull. Inst. Combin.<\/em>, <strong>17<\/strong> (1996), 39-46."},{"key":"key-10.3934\/amc.2016030-25","doi-asserted-by":"publisher","unstructured":"P. R. J. \u00d6sterg\u00e5rd and H. O. H\u00e4m\u00e4l\u00e4inen, A new table of binary\/ternary mixed covering codes, <em>Des. Codes Cryptogr.<\/em>, <strong>11<\/strong> (1997), 151-178.","DOI":"10.1023\/A:1008228721072"},{"key":"key-10.3934\/amc.2016030-26","doi-asserted-by":"crossref","unstructured":"F. Pambianco, D. Bartoli, G. Faina and S. Marcugini, Classification of the smallest minimal 1-saturating sets in $PG(2,q)$, $q\\le 23$, <em>Electron. Notes Discrete Math.<\/em>, <strong>40<\/strong> (2013) 229-233.","DOI":"10.1016\/j.endm.2013.05.041"},{"key":"key-10.3934\/amc.2016030-27","doi-asserted-by":"crossref","unstructured":"F. Pambianco, A. A. Davydov, D. Bartoli, M. Giulietti and S. Marcugini, A note on multiple coverings of the farthest-off points, <em>Electron. Notes Discrete Math.<\/em>, <strong>40<\/strong> (2013) 289-293.","DOI":"10.1016\/j.endm.2013.05.051"},{"key":"key-10.3934\/amc.2016030-28","unstructured":"J. Quistorff, On Codes with given minimum distance and covering radius, <em>Beitr\u00e4ge Algebra Geom.<\/em>, <strong>41<\/strong> (2000) 469-478."},{"key":"key-10.3934\/amc.2016030-29","unstructured":"J. Quistorff, Correction: On codes with given minimum distance and covering radius, <em>Beitr\u00e4ge Algebra Geom.<\/em>, <strong>42<\/strong> (2001), 601-611."},{"key":"key-10.3934\/amc.2016030-30","unstructured":"T. Sz\u0151nyi, Complete arcs in Galois planes: a survey, in <em>Quaderni del Seminario di Geometrie Combinatorie 94<\/em>, Univ. degli Studi di Roma \"La Sapienza'', Roma, 1989."},{"key":"key-10.3934\/amc.2016030-31","doi-asserted-by":"crossref","unstructured":"G. J. M. van Wee, G. D. Cohen and S. N. Litsyn, A note on perfect multiple coverings of the Hamming space, <em>IEEE Trans. Inform. Theory<\/em>, <strong>37<\/strong> (1991), 678-682.","DOI":"10.1109\/18.79931"}],"container-title":["Advances in Mathematics of Communications"],"original-title":[],"link":[{"URL":"http:\/\/www.aimsciences.org\/journals\/displayArticlesnew.jsp?paperID=12788","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T10:07:44Z","timestamp":1772791664000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.aimsciences.org\/\/article\/doi\/10.3934\/amc.2016030"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016]]},"references-count":31,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2016]]}},"URL":"https:\/\/doi.org\/10.3934\/amc.2016030","relation":{},"ISSN":["1930-5346","1930-5338"],"issn-type":[{"value":"1930-5346","type":"print"},{"value":"1930-5338","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016]]}}}